I have some ancient Realstic brand phones like that - good old Radio Shack, they made some decent stuff in the day...
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I like this style, or yours, because you can hammer out a strong treadmill workout and never pop an ear bud, and how anoying is that!
But they're due to be replaced, yours look aces.
I still have an old Aiwa pair (blue, of course!
) with the neck band style, I liked them. Earbuds NEVER stay in my ears, I don't care how many alternate rubber tips they offer, they are all too big and just don't stay in. I have a cheapo boom mike type that hangs over my ear and has a mike in front of my mouth to use when driving (I am not a fan of bluetooth and it's waves doncha know), and that works just fine.
At night I have a pair of "ladies' sports earbuds (I forget the brand, not terribly expensive, got 'em in Target) that has a weird rubber movable tip that actually goes into the ear canal a bit and stays put, sort of like the old cell phone high-end ones I had that sat in my ear the same way. I could still hear everything else, but at least these stay in place.
Oh, how complicated technology can be!